Question

Find a 90% confidence interval for a population mean μ for these values. (Round your answers to three decimal places.)

(a) n = 130, x = 0.82, s² = 0.085

______ to _______

(b) n = 40, x = 22.7, s² = 3.19

______ to ________

Answer 1

Solution :

Given that,

a) n = 130, x = 0.82, s² = 0.085

Point estimate = sample mean = = 0.82

sample standard deviation = s = 0.29

sample size = n = 130

Degrees of freedom = df = n - 1 = 130-1 = 129

t _/2,df = 1.66

Margin of error = E = t_/2,df * (s /n)

= 1.66 * ( 0.29/ 130)

Margin of error = E =0.0421

The 90% confidence interval estimate of the population mean is,

- E < < + E

0.82 - 0.0421 < < 0.82+0.0421

0.778 < < 0.862

(0.778 to 0.862)

(b) n = 40, x = 22.7, s² = 3.19

Point estimate = sample mean = = 22.7

sample standard deviation = s = 1.79

sample size = n = 40

Degrees of freedom = df = n - 1 = 40-1 = 39

t _/2,df = 1.68

Margin of error = E = t_/2,df * (s /n)

= 1.68 * ( 1.79/ 40)

Margin of error = E =0.476

The 90% confidence interval estimate of the population mean is,

- E < < + E

22.7 - 0.476 < < 22.7+0.476

22.2< < 23.2

(22.2 to 23.2)